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Re: Scheper's Catmull-Rom curves, and Spiro curves

From: Dave Crossland <dave@lab6.com>
Date: Thu, 15 Jul 2010 12:28:26 -0400
Message-ID: <AANLkTimgWnZkNETLnQjL6sIUvxQAasPvEfbKInzAYxZq@mail.gmail.com>
To: www-svg@w3.org
On 14 July 2010 18:26, Doug Schepers <schepers@w3.org> wrote:
> Dave Crossland wrote (on 7/14/10 11:47 AM):
>> Responding to the minutes:
>> On 13 July 2010 22:31, Anthony Grasso<anthony.grasso@cisra.canon.com.au>
>>  wrote:
>>>  Catmull-Rom curves
>>>  <shepazu>  http://schepers.cc/?p=243
>>>  DS: If you look at that link. If you compare his spiro curves and mine
>>>  ... his look a lot better
>>>  ... not sure how he does that
>> But its so simple. Here's http://levien.com/phd/thesis.pdf is 191
>> pages of Berkeley math PhD thesis to explain! ;p
> Ah, pretty pictures!  However, the prose was marred by some squiggly
> nonsense shapes that looked something like this: "1 2 3 4 5 6 7 8 9 0".
> I skimmed the paper, and read the intro and conclusion; the section on
> interpolation masters (p. 158, Figures 10.9 and 10.10) was particularly
> interesting.  I think you and I talked about this in Brussels, and I wonder
> how well Catmull-Rom curves would perform in this regard?


>>>  ... the advantage of the Cutmull-Rom curve if you just give a set of
>>> points
>>>  ... It looks like with Spiro curves points have a different
>>> characteristic
>> Spiro has 5 kinds of points.
> So, in that respect, spiro is more akin to a multiple-command path segment
> than to one particular command such as a cubic Bézier.  In other words, my
> experiment with [1] using a combination of (simulated) Catmull-Rom curves
> combined with Linetos is rather similar to spiro.

Without a screencap on your blog, I'm not sure how you authored the
image there.

It strikes me that a mature authoring environment for CR curves looks
a lot like the "auto smooth node" Inkscape point type.

The questions to me are:

Are CR curves as smooth as Spiro curves for the same number of points? - No.

Are CR curves as easy to author smooth curves with as Spiro curves? -
Yes, guess so based on Inkscape auto smooth nodes, unlike normal

Do CR curves interpolate as smoothly as Spiro curves? - I don't know.

> However, he seems like a reasonable guy. :)

I look forward to hearing what he says :)

> [1] http://schepers.cc/?p=243#spiro-a
Received on Thursday, 15 July 2010 16:29:15 UTC

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